Choose all that correctly graph the exponential function.

In order to estimate the mean number of years of formal education for adults in a large urban community, a sociologist took a random sample of 25 adults. The sample mean was found to be 11.7 years, with a standard deviation of 4.5 years. Using this information, a 85% confidence interval for the population mean number of years of formal education needs to be calculated.

To construct a confidence interval, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

First, we need to determine the critical value associated with an 85% confidence level. Since the sample size is small (25), we need to use a t-distribution. For an 85% confidence level with 24 degrees of freedom (25 - 1), the critical value is approximately 1.711.Next, we calculate the standard error by dividing the sample standard deviation (4.5 years) by the square root of the sample size (√25).

Standard Error = 4.5 / √25 = 0.9 yearsFinally, we can construct the confidence interval:Confidence Interval = 11.7 ± (1.711 * 0.9)The lower bound of the confidence interval is 11.7 - (1.711 * 0.9) = 10.36 years, and the upper bound is 11.7 + (1.711 * 0.9) = 13.04 years.Therefore, the 85% confidence interval for the population mean number of years of formal education is (10.36 years, 13.04 years).

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Considering the situation given, it is found that:

At the null hypothesis, we test if they average the same amount of trouble hours as last year, that is, of 2000 trouble hours, thus:

\(H_0: \mu = 2000\)

At the alternative hypothesis, we test if this amount has increased, that is:

\(H_1: \mu > 2000\)

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Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

Number of each type of cards after solving system of equations for given situation of Pedro cards are 29 and68.

Interpretation is Pedro collected 29 football cards and 68 baseball cards.

As given,

Total number of cards=97

Let y=football cards

    x=baseball cards

System of equations are

x + y=97  __(1)

x=y +39    __(2)

Substitute (2) in (1)

y+ 39 +y=97

⇒2y=58

⇒y=29

Substitute y=29 in (2),

x=29 +39

 =68

Therefore, number of each type of cards after solving system of equations are football cards 29 and baseball cards 68.

Interpretation is Pedro collected 29 football cards and 68 baseball cards.

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Answer:

\(y=\frac{1}{2}\)

Step-by-step explanation:

\(4(y+1)= \frac{3}{1-y}\)

\(4y+4= \frac{3}{1-y}\)

\((4y+4)(1-y)= 3\)

\(4y(1-y)+4(1-y)=3\)

\(4y-4y^{2} +4-4y=3\)

\(-4y^{2}=3-4\)

\(4y^{2}=1\)

\(y^{2} = \frac{1}{4}\)

\(y=\sqrt{\frac{1}{4} }\)

\(y=\frac{1}{2}\)

Answer: volume of the cube is (7 cm)^3= 343 cm^3

The cost of 10 cereal bars at the cheaper shop (i.e. at supermarket) = £7.5

We can observe that at corner shop, 5 cereal bars cost 4 pounds.

So, using unitary method, 1 cereal bar costs 5/4 = 0.8 pounds.

And at supermarket, 2 cereal bars cost 1.50 pounds.

so, using unitary method one cereal bar costs 1.5/2 = 0.75 pounds.

This means that supermarket is cheaper than the corner shop.

Now we need to finnd the cost of 10 cereal bars at the cheaper shop i.e., to find the cost of 10 cereal bars at supermarket.

Let us assume that the cost of 10  cereal bars is m pounds.

Using unitary method the cost of 10 cereal bars at supermarket would be:

x = (number of cereal bars) × (cost of each cereal bar)

x = 10 × 0.75

x = 7.5 pounds

Therefore, the cost of 10 cereal bars at the cheaper shop = £7.5

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Find the complete question below.

Karma wants to buy cereal bars from the corner shop or the super market. What is the cost of 10 cereal bars at the cheaper shop?

The probability of observing the experiment result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true is the definition of "P-Value."

A null hypothesis is a sort of statistical hypothesis which asserts that there is no statistical significance in a particular set of observations.

Using sample data, hypothesis testing is performed to determine the believability of a theory. It really is expressed as H0 and is also known to simply as "null."

Some key features regarding null hypothesis are-

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He may be paid less each week if no work is available, option D is correct.

Chris being an hourly employee suggests that he is paid based on the number of hours he works.

He may be paid less each week if no work is available reflects a common practice for hourly employees where their pay may vary depending on the availability of work.

If there is no work available, Chris may receive less pay for that week.

Hence, He may be paid less each week if no work is available, option D is correct.

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Answer:

\( \frac{ {x}^{ - 2} {y}^{ \frac{1}{2} } }{ \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{ {x}^{2} \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{6 {x}^{2}y \sqrt{x} } = \frac{1}{6 {x}^{ \frac{5}{2} } {y}^{ \frac{1}{2} } } = \frac{1}{6} {x}^{ - \frac{5}{2} } {y}^{ - \frac{1}{2} } \)

\( \frac{1}{6} \times - \frac{5}{2} \times - \frac{1}{2} = \frac{5}{24} \)

This is because when there is no correlation, the variation in y cannot be explained by the variation in x, leaving a lot of room for error. the error variance for the linear model

a) If the correlation between x and y is 1, it means that the two variables have a perfect positive linear relationship. In this case, the error variance for the linear model would be 0. This is because when there is a perfect correlation, all the variation in y can be explained by the variation in x, leaving no room for error. Therefore, the error variance would be 0.

b) If the bet correlation ween x and y is 0, it means that the two variables have no linear relationship. In this case, the error variance for the linear model would be the sum of the variances of x and y. This is because when there is no correlation, the variation in y cannot be explained by the variation in x, leaving a lot of room for error. Therefore, the error variance would be the sum of the variances of x and y, which is 49+4=53.

a) If the correlation between x and y is 1, the value of the error variance for your linear model would be 0. This is because a correlation of 1 indicates a perfect positive linear relationship between x and y, meaning there is no error or deviation from the predicted values of y based on the linear model.

b) If the correlation between x and y is 0, the value of the error variance would be equal to the variance of y. This is because a correlation of 0 indicates that there is no linear relationship between x and y, meaning that the linear model provides no predictive value for y. In this case, the error variance is equal to the variance of y, which can be calculated by squaring the standard deviation of y (2^2 = 4).

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Answer:

where is the figure. please provide a figure.

Answer:

\(75 \div 150 \times 100 = \)

50%

Answer: first blank: jen

second blank: mean

Step-by-step explanation:

N/A

Answer:

4.25

Step-by-step explanation:

Since this is a parallelogram, the parallel sides have the same value.

And since the perimeter of a parallelogram is all of the sides combined, this means

WR + RJ + JS + WS, or

5x + 5x + 3x + 2 + 3x +2 = 16x + 4

The perimeter is 16, so

16x + 4 = 16

16x = 12

x = 0.75

Substitute into 3x + 2, or WS.

2.25 + 2 = WS

WS = 4.25

Step-by-step explanation:

perimeter of parallelogram =16

so value of WS=3x+2

hope it helps

Answer: 166 Soft Drinks

Step-by-step explanation:

250 ÷ 1.50 = 166

Answer:

Total change in time is -40 seconds.

Step-by-step explanation:

Answer:

40 seconds

Step-by-step explanation:

Answer:

7 5/12

Step-by-step explanation:

first, subtract 4 5/6 from 6 2/3 by converting 6 2/3 to 6 4/6

5 3/4 + (6 4/6 - 4 5/6) = 5 3/4 + 1 4/6

* I borrowed 6/6 or '1' from the 6 and made 4/6 into 10/6

5 3/4 equals 5 9/12 and 1 4/6 equals 1 8/12

adding them gives you:

6 17/12 which is the same as 6 + 1 5/12, or 7 5/12

Answer:

The answer is 8

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Given

3x + 2(y - 4) ← substitute x = 10 and y = 7 into the expression

= 3(10) + 2(7 - 4)

= 30 + 2(3)

= 30 + 6

= 36

Answer:

See explanation

Step-by-step explanation:

Given:

5⁴/25 = 5²

25 = 5²

Then,

5⁴ / 25

= 5⁴/5²

Note:

• multiplication sign means addition in indices

• Division sign means subtraction in indices

Both numerator and denominator have the same base, so you'll pick one of the bases and subtract the powers

So,

5⁴/5²

= 5^(4 - 2)

= 5^(2)

= 5²

Therefore,

5⁴ / 25 = 5²

Answer:

12(-3x + 2)

Step-by-step explanation:

-1/2 ( 32x - 40) - (20x - 4) = -16x + 20 - 20x + 4 = -36x + 24 = 6(-6x + 4) = 12(-3x + 2)

The value of k for which f(x) is a legitimate pdf is 3.

To determine the value of k for which f(x) is a legitimate probability density function (pdf), we need to ensure that the integral of f(x) over its entire range is equal to 1.

Integrating f(x) over the range x > 1:

∫[1, ∞] (k/x^4) dx = 1

Evaluating the integral:

[-k/(3x^3)] from 1 to ∞ = 1

Taking the limit as x approaches infinity:

[-k/(3x^3)] from 1 to ∞ = -k/(3∞^3) - (-k/(3(1)^3)) = 0 - (-k/3) = k/3

Setting this equal to 1:

k/3 = 1

Solving for k:

k = 3

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Answer:

so it was in my textbook coincidenly here is a solution for that

Step-by-step explanation:

Since,

cos 200°

= 1/sec 200°

⇒ cos 200°

= 1/(-1.0641)

= -0.9397

The true equation would be = DE/DF = AB/AC

What does an equivalent ratio look like?

When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.

Are all proportions an equivalent ratio?

Proportional quantities are represented by a collection of corresponding ratios. We can claim, for instance, that 2:3 and 4:6 are proportionate.

Is proportion a constant?

"X is to Y as A Is to B" is how a proportion is expressed. Cross products are the xb and ay products. A proportion's cross products are consistently equal.

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a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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1. The values of x on the straight line is 28.

2. The value of x in the triangle is 12.

Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line.

The measure of angles on a straight line is 180 degrees.

Therefore,

65 + 4x + 3 = 180

65 + 3 + 4x = 180

68 + 4x = 180

4x = 180 - 68

4x = 112

divide both sides by 4

x = 112 / 4

x = 28

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Hence,

128 = 3x - 2 + 7x + 10

128 = 10x + 8

128 - 8 = 10x

120 = 10x

x = 120 / 10

x = 12

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